Such a braking device is already disclosed in EP-A 247 253 with respect aircraft brakes, but it can also be applied to vehicle brakes. The groups of brakes in this reference are distributed to one or more shafts and are allocated to one or more wheels. The braking device works in such a way that at the beginning of a typical braking, a first group of brakes is applied, and when its temperature achieves the above-mentioned temperature limit, above which damage to the friction brakes could occur, the friction brakes of this first group of brakes are released and the friction brakes of a second brake group are then correspondingly applied. The friction brakes of the first group of brakes can now cool off, and if the friction brakes of the second group of brakes reach the temperature limit, the first group of brakes can be reapplied. Of course, more than two groups of brakes can be provided, in which case the individual groups of brakes are applied consecutively. If all available groups of brakes exceed the temperature limit, that brake group which has the lowest temperature is applied most strongly and the group of brakes which has the highest temperature is applied least strongly in order to achieve cumulatively the braking necessary corresponding to the braking requirement signal. In addition, the known braking device also has measurement devices to determine the achieved braking effect of the individual groups of brakes, which makes it possible to compensate with stronger application of other groups of brakes for drops in braking effectiveness caused, for example, by fading or loss of pressure. But with this known braking device there is still the chance that the friction brakes of the individual groups of brakes will wear out at different rates, so that finally the friction brakes of one group of brakes reach their wear limit while in other groups of brakes the friction brakes still have plenty of wear left. This causes a common, premature, and wasteful replacement of friction materials for the friction brakes of the entire aircraft or vehicle. Another deficiency of the known braking device is that the individual groups of brakes are each applied until they achieve the temperature limit for their friction brakes before they are released. There are, however, many known friction materials which exhibit very poor wear at both low and high temperatures with respect to the temperature limit in a temperature range which may be above 100.degree. C. and up to about 250.degree. C., but which on the other hand have only very limited wear with good friction and therefore braking effects. The friction brakes of the known braking device often work outside of this most advantageous (in terms of wear) temperature range for friction materials.